Quantum model of an autonomous oscillator in hard excitation regime

TL;DR

This paper introduces a quantum model for a nonlinear autonomous oscillator in the hard excitation regime, deriving explicit stationary state populations and identifying three behavioral regimes, with comparisons to soft excitation models.

Contribution

It presents a novel quantum model for a hard excitation regime oscillator, derived from classical equations and solved explicitly for small nonlinearities.

Findings

Three distinct behavioral regimes identified

Explicit solutions for stationary state populations

Comparison with soft excitation quantum oscillator

Abstract

We propose the simple quantum model of nonlinear autonomous oscillator in hard excitation regime. We originate from classical equations of motion for similar oscillator and quantize them using the Lindblad master equation for the density matrix of this system. The solution for the populations of the stationary states of such oscillator may be explicitly found in the case when nonlinearity parameters of the problem are small. It was shown that in this situation there are three distinct regimes of behavior of the model. We compare properties of this model with corresponding ones of close open system, namely quantum oscillator in soft excitation regime. We discuss a possible applications of the results obtained.